Question 407397
Since "The ratio of the measures of the sides of a quadrilateral is 2:3:5:7", we know that the four sides are 2x, 3x, 5x, and 7x units long for some unknown number x.



Because "the figure's perimeter is 68", we can say that {{{2x+3x+5x+7x=68}}}





{{{2x+3x+5x+7x=68}}} Start with the given equation.



{{{17x=68}}} Combine like terms on the left side.



{{{x=(68)/(17)}}} Divide both sides by {{{17}}} to isolate {{{x}}}.



{{{x=4}}} Reduce.



Now that we know that {{{x=4}}}, this means that 


2x=2(4) = 8
3x=3(4) = 12
5x=5(4) = 20
7x=7(4) = 28


Notice that 8+12+20+28 = 68



So the lengths of the 4 sides are: 8, 12, 20, and 28 units.



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